Global analysis and optimal control of a periodic visceral leishmaniasis model

Ibrahim M. ELmojtaba, Santanu Biswas, Joydev Chattopadhyay

Research output: Contribution to journalArticle

Abstract

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R0, the basic reproduction number, is less than unity. When R0 > 1 and under some conditions, then our system has a unique positive ω-periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.

Original languageEnglish
Article number80
JournalMathematics
Volume5
Issue number4
DOIs
Publication statusPublished - Dec 14 2017
Externally publishedYes

Keywords

  • Global stability analysis
  • Non-autonomous system
  • Optimal control
  • Periodic solutions
  • Visceral leishmaniasis

ASJC Scopus subject areas

  • Mathematics(all)

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